Testing for exact model fit and model comparison in structural equation modeling under non-normality
[eng] Structural equation modeling (SEM) is a versatile framework that allows researchers to estimate systems of equations and test theoretical models. A significant portion of the literature on SEM focuses on model fit and selection, where researchers are interested in evaluating the goodness of fi...
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| Format: | doctoral thesis |
| Status: | Published version |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/207990 |
| Online Access: | https://hdl.handle.net/2445/207990 http://hdl.handle.net/10803/690165 |
| Access Level: | Open access |
| Keyword: | Models d'equacions estructurals Structural equation modeling |
| Summary: | [eng] Structural equation modeling (SEM) is a versatile framework that allows researchers to estimate systems of equations and test theoretical models. A significant portion of the literature on SEM focuses on model fit and selection, where researchers are interested in evaluating the goodness of fit of a theoretical model (absolute fit) or comparing multiple plausible models (relative fit). Evaluating exact or approximate fit is possible in both cases. The current doctoral thesis is a compilation of two published studies that contribute to the literature on both absolute and relative fit. The first study aimed to compare the accuracy of assessing exact model fit using two tests, namely the mean and variance adjusted chi-square test and the recently developed robust version of the Standardized Root Mean Squared Residual (SRMR) test, in situations where data is not normal. Through simulation, the study examined the impact of factors such as (non)normality, sample size, and model size on test accuracy. The results showed that the robust chi-square test outperformed the robust SRMR test with respect to Type I error rates and was less affected by model size. The second study investigated the accuracy of evaluating relative model fit using several versions of chi-square difference tests that are robust to violations of normality. The study manipulated levels of (non)normality, sample size, model size, and degrees of freedom for the difference test through simulation. The results showed that the mean and variance adjusted chisquare difference test performed accurately across all investigated conditions and outperformed its mean-adjusted competitors, which required larger samples to perform adequately. In summary, the two studies in the doctoral thesis contribute to the literature on both absolute and relative fit in SEM. The findings suggest that the robust chi-square test is more accurate in assessing exact model fit than the robust SRMR test, and the mean and variance adjusted chi-square difference test is a reliable method for evaluating relative model fit in SEM. |
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